When I had my child care center we stayed open until 2:30 am so the strippers could come get their kids after work. I even had some nurses working the 3-11 shift and they couldn't find child care either so it was really needed.
I had a daytime staff, teacher types, and an evening staff, think crafts and fun activities, that made a bit more per hour. Since I was licensed for 30 and really had split kids I had over 58 kids enrolled. I also was open on Saturdays and Sundays. It really depends on the hours the owner wants to be open.
When I worked in OKC the kids went to a child care center open 24 hours, 7 days a week. After work we would often go out for a while and had to pay extra for the extra hours. Child care is only for about 10 hours a day and anything over that is extra charges. They need your child picked up top make room for the child coming in to take their place in the numbers.
Call your local child care licensing agency or state child care assistance office, ours in OK is called DHS, some other places it's child services or social services. They should have a list of ALL licensed child care places and the hours they are open.